EAGER: Viability study for interfacial spectroscopy

当液滴受到外力作用时，它的形状通常会发生振荡，其频率取决于液滴的材料特性。在一些自然发生的和令人感兴趣的技术过程中，液滴内部含有夹杂物。这些夹杂物可能是小气泡或固体颗粒，会影响液滴的特征振荡。这个EAGER提案的目标是表明，通过测量水滴振荡的频率，可以确定这种内含物的大小、数量和位置。该项目将结合理论、数值计算和实验来证明这一想法的可行性，这被称为“界面光谱学”。该结果可作为涉及油墨、油漆和其他悬浮液等材料的各种处理操作的质量控制工具，或用于检测多相系统中的杂质和污染物。该项目将让高中生和本科生参与实验的设计和实施，以验证该方法。多相系统的自然脉动，如载粒子滴，表现出具有有趣的频率和衰减特征的表面波。最近的研究表明，在一些模式中，稍微偏离的频率会形成类似于原子能级中精细结构分裂的能带。可以证明，这种频率和衰减谱对于多相多种畴的每个内部结构都是唯一的。这表明有可能从实验测量的界面波光谱数据中发现复杂不透明液体内部的物质。这个EAGER项目将确定这种诊断技术的可行性和准确性。该项目将把重点放在四个具体问题上，考虑到含有颗粒的液滴是复杂系统的代表。首先，模拟将证明界面波的频率和衰减常数如何随液滴内粒子的大小、数量和位置而变化。其次，设计一种反演算法，从光谱信息中提取颗粒细节。然后，将诊断程序应用于实际实验中，以测试该技术的能力和局限性。第四，推广反演的唯一性定理，看看是否可以使用该方法揭示更复杂的结构。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

When a liquid drop is subjected to an external force, it typically undergoes oscillations in its shape with a frequency that depends on the material properties of the drop. In some naturally occurring and technological processes of interest, drops contain inclusions in their interior. These inclusions, which could be small bubbles or solid particles, can affect the characteristic oscillations of the drop. The goal of this EAGER proposal is to show that by measuring the frequency of drop oscillations, the size, number and locations of such inclusions can be determined. The project will use a combination of theory, numerical computations and experiments to demonstrate the feasibility of this idea, which is called “interfacial spectroscopy.” The results could be useful as a quality control tool in a variety of processing operations involving such materials as inks, paints, and other suspensions or to detect impurities and contaminants in multiphase systems. The project will involve high-school students and undergraduates in the design and implementation of experiments to validate the approach.Natural pulsations of multiphase systems like particle-laden drops exhibit surface waves with intriguing frequency and decay features. Recent studies have shown that slightly deviating frequencies for a few modes form bands akin to fine-structure split in atomic energy levels. It can be shown that such frequency and decay spectra are unique for each internal structure of the multiphase multispecies domains. This suggests the possibility of finding what is inside a complicated opaque liquid from experimentally measured interfacial wave spectra data. This EAGER project will establish the viability and accuracy of this diagnostic technique. The project will concentrate on four specific matters considering particle-laden drops to be the representative of complex systems. First, simulations will demonstrate how frequencies and decay constants of interfacial waves vary with size, number and position of the particles inside a droplet. Secondly, an inversion algorithm will be devised to extract the particulate details from spectral information. Then, the diagnostic procedure will be applied in real experiments to test the capability and the limit of the technology. Fourthly, the uniqueness theorem for inversion will be generalized to see whether more complex structures can be revealed using the approach.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.